A circle with circumference $14\pi$ has an arc with a $270^\circ$ central angle. What is the length of the arc? ${14\pi}$ ${270^\circ}$ $\color{#DF0030}{\dfrac{21}{2}\pi}$
Answer: The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{360^\circ} = \dfrac{s}{c}$ $\dfrac{270^\circ}{360^\circ} = \dfrac{s}{14\pi}$ $\dfrac{3}{4} = \dfrac{s}{14\pi}$ $\dfrac{3}{4} \times 14\pi = s$ $\dfrac{21}{2}\pi = s$